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Question

ABC is an isosceles triangle right angled at C. Prove that AB2=2AC2.


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Solution

Proving that AB2=2AC2:

ΔABCis an isosceles triangle right angled at C.

In ΔACB,C=90°

AC=BC [By isosceles triangle property]

AB2=AC2+BC2 [By Pythagoras theorem]

AB2=AC2+AC2 [Since, AC=BC]

AB2=2AC2

Hence we proved that AB2=2AC2


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